Numpy

矩阵与数组

In [3]: from numpy import *

In [4]: a = random.rand(4,3)

In [5]: a
Out[5]: 
array([[ 0.18283831,  0.21897507,  0.06911263],
       [ 0.56010641,  0.44530748,  0.96900526],
       [ 0.07938149,  0.83705278,  0.20325507],
       [ 0.90471882,  0.53764717,  0.33122263]])

In [6]: mat(a)
Out[6]: 
matrix([[ 0.18283831,  0.21897507,  0.06911263],
        [ 0.56010641,  0.44530748,  0.96900526],
        [ 0.07938149,  0.83705278,  0.20325507],
        [ 0.90471882,  0.53764717,  0.33122263]])

In [7]: type(a)
Out[7]: numpy.ndarray # 数组类型

In [8]: a = mat(a)

In [9]: type(a)
Out[9]: numpy.matrixlib.defmatrix.matrix # 矩阵类型

In [10]: a
Out[10]: 
matrix([[ 0.18283831,  0.21897507,  0.06911263],
        [ 0.56010641,  0.44530748,  0.96900526],
        [ 0.07938149,  0.83705278,  0.20325507],
        [ 0.90471882,  0.53764717,  0.33122263]])

In [11]: a.I # 矩阵求逆（没有使用方阵，这里是伪逆矩阵）
Out[11]: 
matrix([[ 0.17987522, -0.31261057, -0.73297284,  1.32681177],
        [ 0.19891349, -0.29239699,  1.27986334,  0.02852485],
        [-0.22442968,  1.3461827 , -0.16030736, -0.77399272]])

In [21]: a * a.I # 因为不是方阵，所以没有输出单位阵
Out[21]: 
matrix([[ 0.06093425, -0.02814661,  0.13516338,  0.19534558],
        [-0.02814661,  0.99915636,  0.00405125,  0.00585509],
        [ 0.13516338,  0.00405125,  0.98054541, -0.02811685],
        [ 0.19534558,  0.00585509, -0.02811685,  0.95936398]])

In [1]: from numpy import *

In [4]: a = random.rand(4,4)

In [5]: a
Out[5]: 
array([[ 0.71411637,  0.47290226,  0.55636164,  0.20517478],
       [ 0.3554218 ,  0.90012918,  0.9086697 ,  0.14233483],
       [ 0.33007245,  0.69314144,  0.40207699,  0.07290092],
       [ 0.20740437,  0.83340077,  0.15481733,  0.11737046]])

In [7]: a = mat(a)

In [8]: a * a.I # 结果有误差
Out[8]: 
matrix([[  1.00000000e+00,   0.00000000e+00,  -4.44089210e-16,   1.11022302e-16],
        [ -1.11022302e-16,   1.00000000e+00,   0.00000000e+00,   3.33066907e-16],
        [ -5.55111512e-17,  -2.22044605e-16,   1.00000000e+00,  -1.11022302e-16],
        [ -5.55111512e-17,   0.00000000e+00,   0.00000000e+00,   1.00000000e+00]])

In [9]: eye(4) # 单位阵，array类型
Out[9]: 
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  1.]])

In [13]: myEye = a * a.I

In [14]: myEye - eye(4) # matrix可以直接与array运算
Out[14]: 
matrix([[  0.00000000e+00,   0.00000000e+00,  -4.44089210e-16,   1.11022302e-16],
        [ -1.11022302e-16,  -2.22044605e-16,   0.00000000e+00,   3.33066907e-16],
        [ -5.55111512e-17,  -2.22044605e-16,   0.00000000e+00,  -1.11022302e-16],
        [ -5.55111512e-17,   0.00000000e+00,   0.00000000e+00,   0.00000000e+00]])

In [15]: type(myEye)
Out[15]: numpy.matrixlib.defmatrix.matrix

tile 函数

像铺瓷砖一样扩展数据

In [18]: a = random.rand(2,2)

In [19]: a
Out[19]: 
array([[ 0.69860728,  0.35574496],
       [ 0.80746093,  0.20802703]])

In [20]: tile(a,(2,2)) # 以a为子矩阵扩展数据
Out[20]: 
array([[ 0.69860728,  0.35574496,  0.69860728,  0.35574496],
       [ 0.80746093,  0.20802703,  0.80746093,  0.20802703],
       [ 0.69860728,  0.35574496,  0.69860728,  0.35574496],
       [ 0.80746093,  0.20802703,  0.80746093,  0.20802703]])

argsort函数

返回数组值从小到大的索引值，与原数组shape相同

In [43]: a = random.rand(1,5)

In [44]: a
Out[44]: array([[ 0.13951597,  0.07581534,  0.6957919 ,  0.2080221 ,  0.8629544 ]])

In [45]: a.argsort()
Out[45]: array([[1, 0, 3, 2, 4]]) # 升序排列数组，返回索引

In [47]: a = random.rand(4,2)

In [48]: a
Out[48]: 
array([[ 0.18149948,  0.57567855],
       [ 0.00914879,  0.14953625],
       [ 0.48911966,  0.75737031],
       [ 0.49874594,  0.07773392]])

In [50]: b=a.sum(axis=1) # 按行加和

In [51]: b
Out[51]: array([ 0.75717803,  0.15868504,  1.24648996,  0.57647986])

In [52]: c=a.sum(axis=0) # 按列加和

In [53]: c
Out[53]: array([ 1.17851386,  1.56031903])

In [54]: a.argsort(axis=0) # 按列排序，元素在一列中所占的位置
Out[54]: 
array([[1, 3],
       [0, 1],
       [2, 0],
       [3, 2]])

In [55]: a.argsort(axis=1) # 按行排序，元素在一行中所占的位置
Out[55]: 
array([[0, 1],
       [0, 1],
       [0, 1],
       [1, 0]])

In [56]: a.argsort() # 默认行排序
Out[56]: 
array([[0, 1],
       [0, 1],
       [0, 1],
       [1, 0]])

Numpy.argsort